Calculus Examples

$- \tan (x)$

Step 1

Write $- \tan (x)$ as a function.

$f (x) = - \tan (x)$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

$F (x) = \int - \tan (x) d x$

Step 4

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

$- \int \tan (x) d x$

Step 5

The integral of $\tan (x)$ with respect to $x$ is $\ln (| \sec (x) |)$ .

$- (\ln (| \sec (x) |) + C)$

Step 6

Simplify.

$- \ln (| \sec (x) |) + C$

Step 7

The answer is the antiderivative of the function $f (x) = - \tan (x)$ .

$F (x) =$ $- \ln (| \sec (x) |) + C$